Linear Legend Formula Sheet Slice
Linear Legend
Exam Reference Blueprint • Q3 IA
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1. Slope Formula
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Rise / Run
Example: Points (3, 7) & (-9, 31)
\[ m = \frac{31 - 7}{-9 - 3} = \frac{24}{-12} = -2 \]
2. Slope-Intercept
\[ y = mx + b \]
m = Slope (Rate) b = y-intercept (Start)
Word Problem Clues:
m: "per", "each"
b: "initial fee"
3. Point-Slope Form
\[ y - y_1 = m(x - x_1) \]
Plug in Point (x₁, y₁) & Slope m
Sign Warning (Q11):
Line thru (-1, 4) with m = -2:
y - 4 = -2(x + 1)
Minus a negative becomes a PLUS!
4. Standard Form
\[ Ax + By = C \]
Slope: m = -A/B
- A must be positive.
- No fractions (A, B, C are integers).
- Used for Total Costs (Q13, 19).
Special Lines
HOY Horiz. | m = 0
y = #
VUX Vert. | m = Undef.
x = #
Notation (f(x) = y)
f(-5): Plug -5 into x spot.
f(x)=135: Set eq = 135.
Intercept Secrets
Y-Int (0, y): Set x = 0
X-Int (x, 0): Set y = 0
Always use Coordinates!
Equation from Two Points (Q10, Q17)
1: Find m Use slope formula. Watch for double negatives!
2: Point-Slope Plug m and ONE point into the point-slope form.
3: Solve for y Distribute and solve for y to get y = mx + b.
Domain (x): Width. Scan Left to Right.
Range (y): Height. Scan Bottom to Top.
Linear Legend • Print-Optimized Reference • 2026
